Opened 4 years ago

Closed 3 years ago

#26189 closed defect (fixed)

Intersection of modular abelian varieties gives wrong answer

Reported by: klui Owned by:
Priority: major Milestone: sage-8.8
Component: modular forms Keywords:
Cc: Merged in:
Authors: Kevin Lui Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: 94b9fdd (Commits, GitHub, GitLab) Commit: 94b9fddbaa4a883e88ad4c3e089332506692a8c5
Dependencies: Stopgaps:

Status badges

Description

The intersection code is sometimes wrong. Here's an example:

This is the setup:

sage: d1 = J0(11).degeneracy_map(22, 1)
sage: d2 = J0(11).degeneracy_map(22, 2)
sage: A = (d1-d2).image()
sage: J = J0(22)

This is correct:

sage: J.intersection(A)
(Finite subgroup with invariants [] over QQbar of Abelian variety J0(22) of dimension 2,
 Abelian subvariety of dimension 1 of J0(22))

This is wrong:

sage: A.intersection(J)
(Finite subgroup with invariants [2] over QQbar of Abelian subvariety of dimension 1 of J0(22),
 Abelian subvariety of dimension 1 of J0(22))

Change History (9)

comment:1 Changed 4 years ago by chapoton

#6392 ?

comment:2 Changed 3 years ago by klui

  • Branch set to u/klui/intersection

comment:3 Changed 3 years ago by klui

  • Commit set to f8f372378591c234e574b6dd3e99e768ae8da1f8
  • Status changed from new to needs_review

No code change here. Just a documentation update.

The intersection of 2 abelian varieties, X and Y, is G+A, where G is a finite subgroup with an element in each component and A is the identity component. I don't think there's a canonical way to choose G so that it's a subgroup of X or Y.


New commits:

f8f3723Added documentation explaining what intersection does.

comment:4 Changed 3 years ago by git

  • Commit changed from f8f372378591c234e574b6dd3e99e768ae8da1f8 to 320ffbbfcf8596bf40ef5c5426e061886f26baef

Branch pushed to git repo; I updated commit sha1. New commits:

320ffbbdoc error

comment:5 Changed 3 years ago by klui

  • Authors set to Kevin Lui

comment:6 Changed 3 years ago by tscrim

  • Milestone changed from sage-8.4 to sage-8.8
  • Reviewers set to Travis Scrimshaw

A little tweak to get the punctuation correct:

-        canonical. (see :trac:`26189`). In this following example, ``B`` is a
-        subvariety of ``J``.::
+        canonical (see :trac:`26189`). In this following example, ``B`` is a
+        subvariety of ``J``::

Once done, you can set a positive review on my behalf.

comment:7 Changed 3 years ago by git

  • Commit changed from 320ffbbfcf8596bf40ef5c5426e061886f26baef to 94b9fddbaa4a883e88ad4c3e089332506692a8c5

Branch pushed to git repo; I updated commit sha1. New commits:

94b9fddpunctuation fix as suggested by Travis Scrimshaw

comment:8 Changed 3 years ago by klui

  • Status changed from needs_review to positive_review

Fixed. Thanks for the review!

comment:9 Changed 3 years ago by vbraun

  • Branch changed from u/klui/intersection to 94b9fddbaa4a883e88ad4c3e089332506692a8c5
  • Resolution set to fixed
  • Status changed from positive_review to closed
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